Techniques for reducing delta values of credit risk positions in online trading of credit derivatives

ABSTRACT

Techniques for reducing delta values of credit risk positions in online trading of credit derivatives are disclosed. In one particular exemplary embodiment, a method for reducing delta values may comprise: receiving, in an online trading system of credit derivatives, a plurality of credit risk positions submitted by a plurality of trader clients, each credit risk position having a delta value and a maturity date, wherein each trader client&#39;s submission is unknown to other trader clients: identifying, from the plurality of trader clients, at least two trader clients who hold offsetting credit risk positions on at least two maturity dates; determining delta offsets to be applied to delta values of the credit risk positions held by the at least two trader clients and having the at least two maturity dates, such that an overall delta of each of the at least two trader clients&#39; credit risk positions remains substantially unchanged after the application of the delta offsets; calculating, based on the determined delta offsets, notional amounts of credit derivative trades needed to realize the delta offsets; and executing the credit derivative trades among the at least two trader clients.

CROSS REFERENCE TO RELATED APPLICATIONS

This patent application claims priority to U.S. Provisional ApplicationNo. 60/987,993, filed Nov. 14, 2007, which is hereby incorporated byreference herein in its entirety.

This patent application is related to U.S. patent application Ser. No.10/954,629, filed Sep. 29, 2004, U.S. patent application Ser. No.10/957,217, filed Oct. 1, 2004, U.S. patent application Ser. No.11/837,159, filed Aug. 10, 2007, and U.S. patent application Ser. No.10/316,167, filed Dec. 9, 2002. each of which is incorporated herein inits entirety.

FIELD OF THE INVENTION

Embodiments of the present invention relate generally to online tradingof financial instruments. More specifically, the present inventionrelates to techniques for reducing delta values of credit risk positionsin online trading of credit derivatives.

BACKGROUND OF THE INVENTION

Electronic trading systems, such as Creditex RealTime® Platform, havebrought great efficiency to credit derivative markets. Nowadays, tradersor dealers representing large financial institutions (e.g., banks andfunds) routinely use electronic trading systems to enter into creditderivative transactions involving large notional amounts. Each financialinstitution may hold multiple credit risk positions as a result ofbuying or selling credit derivatives. In the context of a credit defaultswap (CDS), which is the most traded type of credit derivative, a creditcurve may be plotted for a reference entity to show the change in CDSspread as a function of maturity lime. Typical maturities may includebut are not limited to: 6-month, 1-year, 2-year, 3-year, 4-year, 5-year,7-year, and 10-year.

For each CDS position, a delta value may be calculated as a first-orderderivative between the present value (PV) of the CDS contract and acorresponding CDS spread. The delta value may indicate how sensitive theCDS contract is in response to a one-basis-point (bps) move in thecredit curve. A credit risk position, such as one corresponding to a CDScontract, may also be referred to as a delta position.

While being delta neutral overall (i.e., with respect to parallel shiftsin the entire credit curve of a particular reference entity), afinancial institution may still be exposed to short/long credit riskpositions in successive maturities on the credit curve. FIG. 1illustrates this problem. FIG. 1 shows an exemplary bar chart wherebucketed delta values are plotted along a timeline to highlight onebank's credit risk positions at different maturities. Although all thepositive and negative delta values may offset one another and thus addup to almost zero, the large delta variance the large variance of thedelta positions could be problematic to the bank holding these creditpositions. For example, as the credit curve in question changes slopefor different maturity dates, the bank's profit and loss (P&L) will haveto swing accordingly. In addition, the bank may be exposed to defaultgap risk if the delta values toggles between short and long positionstoo quickly in successive maturities.

Some credit derivative dealers have attempted to solve theabove-described problems by engaging one another on a bilateral basis toreduce their risks, i.e., where they are able to find offsettingpositions. While this approach provides some risk reduction benefits, itsuffers from several limitations. For example, this bilateral processrequires “trusted” counterparties due to transparency in disclosure ofpositions. One counterparty can only expect to mitigate risk positionsfor which the other counterparty happens to hold offsetting positions.Overall, the existing approach is labor-intensive, time-consuming,error-prone, and ultimately not scalable.

In view of the foregoing, it may be understood that there aresignificant problems and shortcomings associated with currentrisk-hedging techniques in credit derivative trading.

SUMMARY OF THE INVENTION

Techniques for reducing delta values of credit risk positions in onlinetrading of credit derivatives are disclosed. In one particular exemplaryembodiment, a method for reducing delta values of credit risk positionsin an online trading system of credit derivatives may comprise:receiving, in the online trading system of credit derivatives, aplurality of credit risk positions submitted by a plurality of traderclients, each credit risk position having a delta value and a maturitydate, wherein each trader client's submission is unknown to other traderclients; identifying, from the plurality of trader clients, at least twotrader clients who hold offsetting credit risk positions on at least twomaturity dates: determining delta offsets to be applied to delta valuesof the credit risk positions held by the at least two trader clients andhaving the at least two maturity dates, such that an overall delta ofeach of the at least two trader clients' credit risk positions remainssubstantially unchanged after the application of the delta offsets;calculating, based on the determined delta offsets, notional amounts ofcredit derivative trades needed to realize the delta offsets; andexecuting the credit derivative trades among the at least two traderclients.

In another particular exemplary embodiment, an electronic trading systemof credit derivatives may comprise: a processor; at least one storagedevice coupled to the processor; a user interface coupled to theprocessor via one or more communication networks. The processor may beadapted to communicate with the at least one storage device and the userinterface to execute instructions to perform the following tasks;receiving, in the online trading system of credit derivatives, aplurality of credit risk positions submitted by a plurality of traderclients, each credit risk position having a delta value and a maturitydate, wherein each trader client's submission is unknown to other traderclients; identifying, from the plurality of trader clients, at least twotrader clients who hold offsetting credit risk positions on at least twomaturity dates; determining delta offsets to be applied to delta valuesof the credit risk positions held by the at least two trader clients andhaving the at least two maturity dates, such that an overall delta ofeach of the at least two trader clients' credit risk positions remainssubstantially unchanged after the application of the delta offsets;calculating, based on the determined delta offsets, notional amounts ofcredit derivative trades needed to realize the delta offsets; andexecuting the credit derivative trades among the at least two traderclients.

One technical effect of the systems and methods of the present inventionis that they facilitate more efficient electronic trading of creditderivatives on modern computers and communications systems. Anothertechnical effect of the systems and methods of the present inventionlies in the specialized computer and communication devices and softwareprograms that may be configured and deployed to carry out the deltaneutral auction functions and other techniques for reducing delta valuesof credit risk positions disclosed herein.

The present invention will now be described in more detail withreference to exemplary embodiments thereof as shown in the accompanyingdrawings. While the present invention is described below with referenceto exemplary embodiments, it should be understood that the presentinvention is not limited thereto. Those of ordinary skill in the arthaving access to the teachings herein will recognize additionalimplementations, modifications, and embodiments, as well as other fieldsof use, which are within the scope of the present invention as describedherein, and with respect to which the present invention may be ofsignificant utility.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to facilitate a fuller understanding of the present invention,reference is now made to the accompanying drawings, in which likeelements are referenced with like numerals. These drawings should not beconstrued as limiting the present invention, but are intended to beexemplary only.

FIG. 1 shows a bar chart illustrating a hypothetical bank's exposure toshort/long credit risks in successive maturities.

FIG. 2 is a flow chart illustrating an exemplary method of reducingdelta values of credit risk positions in accordance with one embodimentof the present invention.

FIG. 3 shows a numerical example of a delta netting process involvingtwo trader clients in accordance with one embodiment of the presentinvention.

FIGS. 4A-4C shows a numerical example of a delta netting processinvolving multiple trader clients in accordance with one embodiment ofthe present invention.

FIG. 5 shows a bar chart illustrating a reduction of delta values aftera delta netting process in accordance with one embodiment of the presentinvention.

FIG. 6 shows a numerical example of multiple-leg delta weighted switchesin accordance with one embodiment of the present invention.

FIG. 7 shows another numerical example of multiple leg delta weightedswitches in accordance with one embodiment of the present invention.

FIG. 8 shows a numerical example illustrating a mid fixing process inaccordance with one embodiment of the present invention.

FIGS. 9-13 show exemplary screenshots of a delta netting process in anonline credit derivative trading system in accordance with oneembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention solve the above-described problemsin existing risk-hedging techniques by providing an auction mechanismthat offers such benefits as risk reduction, trader anonymity, matchingefficiency, and straight-thru-processing (STP). In particular, a suiteof delta-reduction or delta-netting functionalities may be implementedin or with an online credit derivative trading system to helpdealers/traders anonymously and efficiently flatten their deltapositions for a series of maturities.

As mentioned earlier, each credit risk position may have an associateddelta value. A delta value of a CDS contract at a particular maturitymay be typically calculated in two steps. First, a first (i.e.,original) present value (PV) of the CDS contract may be calculated basedon its corresponding credit curve. Then, the credit curve may be shiftedby one basis point at some maturity, and a second (i.e., new) PV of theCDS contract may be calculated. The difference between the first and thesecond PV may be used to represent the delta value of the CDS contractat the particular maturity. By calculating and then summing delta valuesfor all of a trader client's credit risk positions, a net or overalldelta value may be determined for the trader client. A “delta neutralauction” refers to an auction process in at least a part of which a netor overall delta value of a trader client's credit risk positionsremains substantially unchanged despite that trader client'sparticipation in trades.

Referring to FIG. 2, there is shown a How chart illustrating anexemplary method of reducing delta values of credit risk positions inaccordance with one embodiment of the present invention. The method istypically implemented in connection with an online trading system ofcredit derivatives, such as Creditex RealTime® Platform.

In step 202, a group of reference entities may be selected as subject ofan upcoming auction session, and the auction session may be scheduled.While it is possible to include reference entities from all sectors in asingle auction session, it is more preferable to focus on only a limitednumber of reference entities in each auction. One concern may be thatincluding a large number of reference entities in any given auctionsession will place a larger burden on traders and trading assistants toupload positions and monitor auction results. Thus, according to oneembodiment of the present invention, one sector of credit derivatives ora subset thereof may be selected for inclusion in each auction session.That is, sector-specific auction sessions may be scheduled for a seriesof different dates. For example, a first auction session for Financialsector credit derivatives may be scheduled on November 16, a secondauction session for Automotive sector may be scheduled on November 30,and so on. According to another embodiment, traders and dealers may beallowed to propose their top choices of reference entities for inclusionin an upcoming auction session. For example, each trader client mayidentify the top 20 reference entities to be included, with or withoutsector limitations. Then, the trading system may determine a final listof reference entities based on the trader proposals and publish thefinal list sometime prior to the auction session. The trading system mayimpose selection rules to ensure a broad coverage of reference entities,for example, by excluding those reference entities that have alreadybeen included in an auction within the past three months.

Of course, the scope of coverage may depend on the trading system'scapacity and/or trader preferences. If desired, each auction participantmay be allowed to submit credit risk positions on any and all referenceentities without sector restriction or numerical cap. The auctionparticipants may also be required to submit a credit curve for eachreference entity.

In step 204, trader clients may be invited to upload their credit riskpositions and marks to the trading system. The uploading may beconducted via a simple yet flexible process. The positions and marks maybe first prepared off-line by traders and trading assistants andcompiled into a spreadsheet format (e.g., Microsoft® Excel). As long asthe spreadsheets include requisite columns for each position and mark,the trading system can easily map the columns to the requiredinformation fields. For a credit risk position, the requisite columnsmay include: Reference Entity Name, Seniority, Maturity, and Amount. TheAmount may be either a delta value at Maturity or an equivalent net CDSnotional amount. Additionally the Amount may be uploaded as either arisk position or a hedge position. For a mark, the requisite columns mayinclude: Reference Entity Name, Seniority, Maturity, Bid, Offer, and/orMid. The Mid refers to a proposed mid-fixing price level for tradeexecution. Alternatively, the trader clients may choose to upload theiroriginal trades, and the trading system may calculate their deltapositions in relevant reference entities.

Once the uploaded spreadsheets are mapped to information fields readableby the trading system, the credit risk positions and marks may bevalidated in step 206. For example, the trading system may automaticallyidentify invalid reference entities (e.g., incorrect names and/orcorrect names not supposed to be in current auction session). Validreference entity names may be mapped or converted to a standard textstring. The validation process may also include highlighting ofsubordinated reference entities, identification of odd maturity dates(i.e., those other than the IMM dates), and identification of invalidnotional amounts (e.g., less than zero or in excess of a billion). IMMstands for the International Monetary Market, and the IMM Dates are thefour dates of each year (i.e., March 20, June 20, September 20, andDecember 20) which most credit default swaps use as their scheduledtermination date.

In some instances, especially if the submitted positions resulted fromtrades previously conducted via the trading system and/or its associatedtrade-capture system, the trading system may already have information onthe reference entities and can easily confirm or verify the positionsand associated credit curves.

In step 208, at or near a designated auction start time, the tradingsystem may automatically run a matching algorithm to identify potentialtrades, switches, or terminations of offsetting positions held bydifferent trader clients. A number of approaches may be taken toautomate the matching process in accordance with embodiments of thepresent invention.

One exemplary approach may be for trader clients to submit a list oftrades they would like to execute in an attempt to reduce or flattentheir delta positions. The trading system may then match notionalamounts of the submitted trades in a pro-rata fashion. That is, for anysingle reference entity and maturity combination, the system may executetrades such that each dealer on either side of the orders would get itsorder filled in the same relative amount to the other dealers on thesame side of the order book.

For example, consider the following where submissions are two buy orderstotaling $3 MM and three sell orders totaling $7 MM:

Bank Order Direction Order Size (SMM) A Buy 1 B Buy 2 C Sell 1 D Sell 2E Sell 4

In this case, the most that can be traded is $3 MM as this is thesmaller of the total buy amount and the total sell amount. Using apro-rata matching process, orders may be filled based on the followingrelation:

-   for each bank.

${{Buy}\mspace{14mu} ({Sell}){\mspace{11mu} \;}{fill}} = {\frac{{{Buy}{\mspace{11mu} \;}({Sell})}{\mspace{11mu} \;}{order}\mspace{14mu} {size}}{{Total}\mspace{14mu} {Buy}\mspace{14mu} ({Sell})\mspace{14mu} {order}\mspace{14mu} {size}} \times {Total}{\mspace{11mu} \;}{amount}\mspace{14mu} {tradable}}$

-   or, in mathematical notation:

$f_{i} = {\frac{o_{i}}{\sum\limits_{j = 1}^{n}o_{j}} \times t_{\max}}$

wherein f_(i) is the fill amount for dealer i on either the buy or sellside (whichever is currently under consideration), o_(i) is the originalorder side for the dealer, n is the number of orders on the buy or sellside, and t_(max) is the maximum amount tradable.

Using the above exemplary set of orders, the simple pro-rata matchingresults for Banks A through E should be as follows:

Bank Order Direction Order Size (SMM) Fill (SMM) % Fill A Buy 1 1  100%B Buy 2 2  100% C Sell 1 0.43 42.9% D Sell 2 0.86 42.9% E Sell 4 1.7142.9%As can be seen, on either side of the order book, each bank gets itsorder filled in the same relative amount as the other banks.

The advantages of the pro-rata matching method may include: (1) it issimple; (2) each credit/maturity can be considered in isolation; and (3)it is fair—no one bank lakes priority over another. However, there arealso some disadvantages. For example, it is not delta neutral: it doesnot preserve the trader's overall delta value for the credit inquestion. For a case where there is a single buy (sell) order andmultiple sell (buy) orders, it would be possible for the single buy(sell) side dealer to see relatively who had the largest position tofill. For example, consider the case where there is a single seller withan order size of $3 MM and three buyers with orders of $1 MM, $2 MM and$3 MM, respectively. Using pro-rate filling of orders would lead to theseller executing trades with the following sizes: $0.5 MM, $1 MM, and$1.5 MM, from which the seller could see that the third counterparty hadthe largest original position. Of course, the seller in this case wouldnot necessarily know that it was the only seller or that the tradesexecuted relied the relative positions of the counterparties.

One approach that preserves delta neutrality whilst reducing oreliminating individual delta values at different maturity buckets is touse a delta-netting procedure. As will be described in more detailbelow, the delta-netting procedure may involve identifying at least twotrader clients who hold offsetting credit risk positions on at least twomaturity dates and then applying delta offsets to delta values of thecredit risk positions held by the at least two trader clients and havingthe at least two maturity dates, such that an overall delta of each ofthe at least two trader clients' credit risk positions remainssubstantially unchanged after the application of the delta offsets.According to one embodiment of the present invention, when the tradingsystem searches for two delta positions that offset each other, a gapbetween the two maturities may be limited, for example, to a certainnumber of months or years. For instance, a 12-month gap limit may beimposed. When a first delta position may be offset against either asecond delta position whose maturity is 9 months apart from that of thefirst delta position or a third delta position whose maturity is 18months apart from that of the first delta position, the trading systemmay select the second delta position instead of the third deltaposition.

Another approach for reducing or eliminating individual delta values maybe to selectively terminate, in whole or in part, some credit derivativetransactions. This may be achieved by setting up an optimizationprocedure wherein the variables are the notional amounts of originaltrades and the objective of the optimization is to minimize the totalnotional amount. Constraints may be added to the optimization algorithmto ensure: (a) each dealer's total PV can change within a specifiedrange of values; (b) each dealer's total delta can change within aspecified range of values; and (c) each dealer's delta at all maturitiescan change, such that, if the current delta is negative, it can changeto a slightly more negative amount but can increase to zero, and, if thecurrent delta is positive, it can change to a slightly more positiveamount but decrease to delta. Constraint (c), along with the objectiveof minimizing total notional across all trades, may enable theoptimization procedure to emulate a delta neutral auction (DNA). Thatis, by allowing delta positions at any maturity to change to be closerto zero and by constraining the total delta to move in a small range ofvalues, the optimization procedure ensures (to some extent) deltaneutrality of the resulting set of trades, while simultaneously reducingthe variance of delta values for a dealer.

By minimizing total notional, it is possible that a significant numberof trades will have their notional amounts reduced to zero, which meanstheoretically that those trades can be terminated. However, because ofthe constraints in place on PV and delta (i.e., Constraints (a) and(b)), there will be some trades that can only be partially terminatedand others that will remain.

Referring back to FIG. 2, in step 210, one or more price levels may bedetermined for trades to be executed. Regardless of what matchingalgorithm is employed in step 208 above, a fair methodology is desirablefor executing any resulting trades at a fair market level. According tosome embodiments of the present invention, the fair market level may beestablished based on a third-party benchmark. For example, pricing datafrom independent providers of dealer “consensus” pricing or aggregatorsof dealer data may be used as a basis or reference to determine a pricelevel. Potential data providers may include Markit Group Limited, FitchRatings (CDS Pricing), and/or CMA Data Vision.

According to other more preferable embodiments of the present invention,the fair market level may be determined through a “mid-fixing” process.First, each participant may be invited to submit a bid and/or offerprice level for each position it wishes to execute (or alternatively forevery full year point on the credit curve). Alternatively, a participantmay submit a mid price, and from that mid price the trading system maysynthesize a bid and offer, for example, by subtracting from and addingto the submitted mid a predetermined value (e.g., 1 bps). The submissionmay be made electronically and limited to a lime window. Second, uponclosing of the time window, Creditex® Mid Fixing algorithm may beapplied to the submissions to determine a trade level for each full yearpoint on the curve. Third, trade levels for fractional maturities may bedetermined using linear interpolation between two consecutive full yearpoints.

The Creditex® Mid Fixing algorithm has been described in prior, relatedapplications which are incorporated herein by reference. Here below is abrief description of this algorithm with a numerical example illustratedin FIG. 8. The description will make reference to the following definedterms:

-   -   “Contributed Market”—The two-way prices contributed by each        individual dealer;    -   “Matched Market”—A bid and offer that are in the same place        (row) in the queue after sorting the bids and offers;    -   “Crossing Market”—a Matched Market in which the bid of one        dealer is higher than the offer of another dealer;    -   “Touching Market”—a Matched Market in which the bid of one        dealer is equal to the offer of another dealer; and    -   “Tradable market”—either a Crossing or Touching Market.

In FIG. 8, the Contributed Markets are listed in the table on the left.

First, bid/offer prices submitted by participants are sorted to matchthe best (highest) bids with the best (lowest) offers. That is, the bidprices are sorted in an ascending order and the offer prices are soiledin a descending order. In case of a tie, prices entered first are placehigher in the queue. In FIG. 8, the sorted bid/offer prices are listedin the table on the right. From top to bottom, the bids decrease and theoffer increase. There are 8 Matched Markets, among which the first twoare Crossing Markets and the third is a Touching Market.

Next, all the tradable markets (where the bid is greater than or equalto the offer) are discarded. That is, the first three Matched Markets inthe Sorted table of FIG. 8 are thrown out, which leaves behind the nextlive Matched Markets.

Then, the best half of the remaining Matched Markets is identified andan average of those bids and offers in the best half is calculated to bethe Mid Fixing price.

Whether the price levels are established through third-party benchmarksor mid-fixing processes, the price levels are typically limited to theIMM maturity dates with the following tenors: 6-month, 1-year, 2-year,3-year, 4-year, 5-year, 7-year and 10-year. To obtain price levels forintermediate dates between consecutive IMM dates, it may be desirable tofollow the market standard convention and use a linear interpolation.Alternatively, participating dealers may provide marks at one or moreintermediate maturities.

Referring back to FIG. 2, in step 212, the credit derivative trades maybe executed and the trade data may be passed on to an automated tradecapture and processing system. As a result, participants would not berequired to manually enter trades generated by the auction into theirrespective trade capture systems. A manual entry approach would requiresignificant lime from traders and trading assistants and may expose allparticipants to operational risks due to errors in trade booking. Theonline trading system in which the auction session takes place mayalready provide straight-thru-processing (STP) capabilities for regulartrades and may be adapted to support automated trade capture of theauction-generated trades.

As briefly described above, a delta-netting process that preserves deltaneutrality for the trader clients may be a preferred approach to matchoffsetting positions among two or more trader clients. It should benoted that, in the context of the present invention, delta neutrality isnot an absolute requirement in the sense that the net change in atrader's overall delta value has to be zero. Rather, if the net changein an overall delta value is within a sufficiently small range (e.g., nomore than 100 or otherwise within an acceptable range as determined bytraders or the trading system), then the auction process may be referredto as delta neutral.

FIG. 3 shows a numerical example of a delta netting process involvingtwo trader clients (Bank A and Bank B) in accordance with one embodimentof the present invention. As shown in the table on the left side. Bank Aand Bank B may have each submitted a plurality of delta positions formaturity dates between Mar. 20, 2010 and Sep. 20, 2014.

Note that, for maturity of 20 Dec. 2010, Bank A is long delta and Bank Bis short delta. However, for 20 Mar. 2014. Bank A is short delta andBank B is long delta. These four delta positions are highlighted in asimplified table on the top right of FIG. 3. Thus, all four of thesedelta positions may be reduced by executing two CDS trades withidentical delta offset values between these two banks, one for each ofthese two maturities. That is, Bank A would buy protection from Bank Bfor the 20 Dec. 2010 maturity and sell protection to Bank B for the 20Mar. 2014 maturity.

In a more general case, the delta netting process may be run to searchfor delta values i=1.2 for two banks (i=1, 2, for Bank A and Bank Brespectively) and two dates (j=1, 2) that satisfy the following:

δ_(1,1)δ_(2,1)<0

δ_(2,1)δ_(2,2)<0

δ_(2,2)δ_(1,2)<0

That is to say, EITHER:

δ_(1,1) & δ_(2,2) are negative and δ_(2,1) & δ_(1,2) are positive, OR

δ_(1,1) & δ_(2,2) are positive and δ_(2,1) & δ_(1,2) are negative.

If a constraint is imposed such that no bank can have an individualdelta position that changes sign, the delta offset value to be appliedto the individual delta positions would have the smallest absolute deltavalue among the original delta positions. In the numerical exampleillustrated in FIG. 3, the delta position having the smallest absolutevalue belongs to Bank A and has a maturity of Mar. 20, 2014. which is−9,115.48. For delta netting, delta offset values of either +9,115.48 or−9,115.48 may be applied to the four delta positions held by Bank A andBank B on the 20 Dec. 2010 and 20 Mar. 2014 maturity dates.Specifically, a −9,115.48 delta offset is applied to Bank A's 20 Dec.2010 position and Bank B's 20 Mar. 2014 position, and a +9,115.48 deltaoffset is applied to Bank A's 20 Mar. 2014 position and Bank B's 20 Dec.2010 position. That is, the same amount of delta offset is added to onematurity but subtracted from another maturity for each bank. As aresult, the absolute delta values of all four positions are reduced,with Bank A's 20 Mar. 2014 position reduced to zero. At the same time,since the net delta offset applied to each bank's positions is zero, theoverall delta for each bank remains unchanged.

Once the delta offset values have been determined, the notional amountsof the trades (i.e., Bank A buys from Bank B for the 20 Dec. 2010maturity and sells to Bank B for the 20 Mar. 2014 maturity) may becalculated based on a “01 per million” factor. The “01 per million”factor is the delta value for a prototypical CDS contract of $1 MMnotional. For the numerical example in FIG. 3, the “01 per million” maybe 291.52 for the 20 Dec. 2010 maturity and 545.90 for the 20 Mar. 2014maturity. For each maturity date, the notional amount of the requiredtrade may be obtained by dividing the delta offset value with thecorresponding “01 per million.” Thus, the notional amount to be tradedis $31.3 MM for the 20 Dec. 2010 maturity and $16.7 MM for the 20 Mar.2014 maturity.

FIGS. 4A-4C shows a numerical example of a delta netting processinvolving multiple trader clients in accordance with one embodiment ofthe present invention.

The delta-netting process described above for an individual pair ofdealers may be extended to multiple counterparties. In a multilateralcase, a similar delta-netting algorithm may be run to search for allcombinations of pairs of banks and pairs of maturities, wherein thefirst bank is long (short) at one maturity and short (long) delta atanother maturity, and the other bank is the other way around. Deltaoffset values may then be applied to the delta positions that fit theabove-described pattern. The algorithm may keep on looking for deltapositions that fit this pattern until it can no longer make any changes.According to one embodiment, in practice, it may be advisable to firstfilter out small delta values below a certain threshold (say less than100). Without this initial filtering, the algorithm might create lots oftrades in small notional amounts.

FIG. 4A shows original delta positions as submitted by five banks, BanksA-E. While the total (net) delta value for each bank is small (no morethan 224), the total absolute delta and the variance are quite large. Asmentioned above, it may be desirable to filter out small delta values—inthis case, delta positions with absolute values less than 100 may be setto zero. Thus, FIG. 4B shows a filtered set of delta positions held byBanks A-E. Note that the total (net) delta value for each bank does notchange significantly even after the small deltas are filtered out. Next,the above-described delta-netting process may be iteratively run on thefiltered set of delta positions, and the resulting delta positions arelisted in a “Netted Deltas” table in FIG. 4C wherein the shaded cellsare those delta positions which have been either reduced (in an absolutesense) or eliminated. Comparing the total (net) delta values, the totalabsolute delta values, and the variance of the delta values beforeversus after the netting procedure, it may be noted that the total netdelta values remain substantially unchanged for all the banks, while thetotal absolute delta values and the variance are significantly reduced.On average, the reduction in the absolute delta values is 32%, and theaverage reduction of the variance is 31%.

As a result of the delta netting procedure with this hypothetical data,47 individual CDS trades are to be executed. Note that there are not aneven number of trades in this case as the netting algorithm also netsthe CDS trades as they are created.

According to embodiments of the present invention, this delta nettingprocess may be able to achieve a relatively greater reduction in curvepositions when (a) there are a larger number of dealers participatingand (b) the participating dealers have many non-zero bucketed deltas.

FIG. 5 shows a bar chart illustrating a reduction of delta values aftera delta netting process in accordance with one embodiment of the presentinvention. Compared to the original delta values, the netted deltavalues are made smaller to various extents.

The delta-netting approach may employ some standard analytics (e.g.,discount and CDS default probability curve construction) to allow thedelta adjustments that lake place during the netting process to beconverted into notional amounts. The interest rate and CDS curvebuilding procedures, and the subsequent discounting and risk-neutraldefault probabilities that are used in the exemplary calculations abovecompare favorably with other analytics packages such as those providedby Bloomberg, I.P.

There are many variations of the above-described delta-nettingprocedure. With the common goal of reducing individual delta valueswhile keeping an overall or net delta value of each trader client withina limited range, a computer-implemented trading system may search foroffsetting delta positions and apply delta offset values in a number ofdifferent ways.

FIG. 6 shows a numerical example of multiple-leg delta weighted switchesin accordance with one embodiment of the present invention. In FIG. 6,filtered delta positions of Traders A through E are listed for multiplematurity dates. A search may be conducted to identify a series ofoffsetting positions held by a number of traders for a number ofmaturities wherein the series of positions may form a closed “path” or“loop.” Note that the six shaded cells present an opportunity for deltanetting among Traders B, C and E. Note also that the arrows connectingthese six cells form a looped path and, along the path, the deltapositions alternate signs. For each of the maturities 20 Mar. 2010, 20Mar. 2011, and 20 Sep. 2013, two of the three traders have offsettingpositions. In addition, for each of the three traders, its delta valueshave different signs on the two maturities highlighted. These six deltavalues are shown in the following 3×3 matrix:

$\delta_{filtered} = \begin{Bmatrix}{{- 18},354.13} & {7,683.70} & \ldots \\\ldots & {{- 1},265.80} & {13,966.94} \\{71,081.58} & \ldots & {{- 15},340.77}\end{Bmatrix}$

The smallest absolute delta value among the six positions is Trader C'sat maturity 20 Mar. 2011, i.e., −1.265.80 at center of the matrix.According to an embodiment of the present invention, this smallestabsolute delta value 1,265.80 may be added or subtracted from the sixdelta positions, as shown below:

${\Delta \; \delta} = \begin{Bmatrix}{{+ 1},265.80} & {{- 1},265.80} & \; \\\; & {{+ 1},265.80} & {{- 1},265.80} \\{{- 1},265.80} & \; & {{+ 1},265.80}\end{Bmatrix}$

$\delta_{netted} = {{\delta_{filtered} \oplus {\Delta \; \delta}} = \begin{Bmatrix}{{- 17},088.33} & {6,417.90} & \ldots \\\ldots & 0.00 & {12,701.14} \\{69,815.78} & \ldots & {{- 14},074.97}\end{Bmatrix}}$

As a result, three trades may be executed for the three respectivematurities in order to realize these delta values (Δδ).

A same or similar delta-netting process as illustrated in FIG. 6 may berepeatedly applied to the delta matrix. That is, the netted delta matrixmay be again searched to identify a similar pattern and accordinglyanother set of delta offset values be applied. The delta-netting processmay be repeated until no more delta positions can be offset or when thedelta variance (or total absolute delta) falls below a predeterminedthreshold.

The delta-netting process as illustrated in FIG. 6 may also be extendedto a series of eight (or 2N) delta positions held by four (or N) tradersfor four (or N) maturities. For example, the above-mentioned closed-looppath may be formed in a delta matrix (i.e., a set of filtered deltavalues) by starting from a first delta position and hopping 2N timesthrough N-1 other delta positions and finally back to the first deltaposition. The first hop is in a horizontal direction (i.e., in the samerow as the first delta position), the second hop is in a verticaldirection from the second delta position, the third hop is in ahorizontal direction from the third delta position, and so on. The last(2N-th) hop is from a 2N-th delta position vertically to the first deltaposition, which means both the 2N-th delta position and the first deltaposition are held by the same trader. In addition, the delta valuesalong the 2N-hop path alternate in signs. With this pattern, deltanetting may be achieved simultaneously for the N traders by executing Ntrades for the N maturities.

FIG. 7 shows another numerical example of multiple leg delta weightedswitches in accordance with one embodiment of the present invention.Similar to the example shown in FIG. 6, three banks (Banks X, Y, and Z)may be identified as holding offsetting positions involving threematurity dates (Maturities 1-3). What is different is that the trades torealize delta offsets may be executed among three banks for some of thematurities. To illustrate an ideal pattern, the delta positions in FIG.7 are shown in multiples of δ in the delta matrix on top of the page.Then, a 3×3 matrix with non-uniform delta offset values may be appliedto the delta matrix, reducing all the delta values to zero in adelta-neutral fashion. To realize the delta offsets, a trade involvingBank X, Bank Y, and Bank Z at Maturity 1 is to be executed where Bank Xsells to both Bank Y and Bank Z. Similarly, for Maturity 3, Bank X maybuy from both Bank Y and Bank Z.

The above description covers a number of exemplary matching techniquesthat can be used to reduce delta values of credit risk positions forvarious traders. It should be noted that some or all of these techniquesmay be combined or alternated when processing multiple delta positionsheld by multiple trader clients. For example, according to embodimentsof the present invention, one delta-neutral matching technique may becombined with another delta-neutral technique or a non-delta-neutraltechnique. For instance, an auction process may start a first round ofdelta reduction with a delta-neutral algorithm and then apply the simplepro-rata matching algorithm in a second round to the netted deltas thatresult from the first-round of delta netting. Similarly, thedelta-netting methods (and/or variations thereof) involving two traderclients, such as those illustrated in FIGS. 3 and 4A-4C, may be appliedto a delta matrix simultaneously or alternatively with the delta-nettingmethods (and/or variations thereof) involving multiple trader clients,such as those illustrated in FIGS. 6 and 7.

FIGS. 9-13 show exemplary screenshots of a delta netting process in anonline credit derivative trading system in accordance with oneembodiment of the present invention. In general, the delta nettingprocess may be carried out in a plurality of stages including apre-submission phase, a submission phase, a mid review phase, and atrade review phase.

FIG. 9 shows a screenshot of what a trader sees during thepre-submission phase. The pre-submission phase may last a relativelylong period of time such as a few hours prior to the official start ofthe delta netting process (also referred to as a delta neutral auctionor “DNA” as indicated in the top-right corner of the screen). Thegraphical user interface (GUI) may include a number of pull-down menus,checkboxes, spreadsheets, charts, and other items to facilitate both thedisplay of information to the trader and the input of data from thetrader. For example, an “Auction Starts” count-down clock maycontinuously remind the trader of the lime remaining until the auctionstarts. A “Maturity Limit” pull-down menu may allow the trader to limitthe gap between two trades in any potential switch. A “Positions”pull-down menu may allow the trader to specify whether the credit riskpositions uploaded are in terms of net notional or delta value.

In addition, when a trader first starts uploading its risk positions, apop-out window or a similar visual prompt may force the trader to answera simple yet critical question as to what a positive delta (or apositive net notional) and a negative delta (or a negative net notional)mean to the trader (or its organization) in terms of buying or sellingcredit protection. It has been discovered that different traders andorganizations may view the meaning of positive and negative delta valuesquite differently. Some may view a negative delta as necessitating asell while others may view the same as requiring a buy. To resolve thisproblem, the online credit derivative trading system may normalizetrader clients' views of “risk” vs. “hedge” by querying each trader whoattempts to participate in the DNA auction process. Based on theresponse received, the system will understand and remember how thetrader views its positions and may process that trader's risk positionsaccordingly.

Referring back to FIG. 9, a first spreadsheet on top side of the screenmay display one or more reference entities available for the upcomingDNA auction and dynamically update information related to thoseentities. A second spreadsheet toward lower left of the screen providesspace for the trader to upload his risk positions with respect to thereference entities. The upload of risk positions may be performedmanually one line at a time or may be through a batch (automated)operation such as copying-and-pasting or converting from an Microsoft®Excel spreadsheet or from any other application that supports TAB or CSVdelimited interchange via the system clipboard.

Traders may be able to upload their risk positions in either thepre-submission phase or the submission phase. Traders may be required toenter either a mid or a bid-offer combination for each maturity bucketon a reference entity name that they wish to reduce their risk on. If nomid or bid/offer is entered, the trader does not have the opportunity tosee the DNA mid (to be displayed in subsequent phases) nor is the traderable to submit a delta position. The trader can choose to enter mids forstandard terms only, and the mids for remaining maturities will begenerated using linear interpolation. The trader may be able to edit anyinterpolated mid. In addition to entering a mid, a trader can enter adelta position or net notional for each maturity bucket on a referenceentity name for which they wish to reduce their risk on. Addingdelta/net notional values is optional during pre-submission orsubmission phases. If no values are entered during these phases, thetrader has an opportunity to edit the delta values or net notionals inthe mid review phase prior to calculating the DNA switch trades.

In FIG. 10, which shows a screenshot of the submission phase, thecount-down clock is showing less than seven minutes before the officialsubmission phase ends. As shown in the second spreadsheet, the traderhas entered a mid for each maturity on the reference entity VLVY (VolvoAB) as well as desired net notionals for some of the maturity dates. Onthe right side of the screen, a first chart entitled “Curves” hasplotted out a first curve corresponding to the trader's input. Oncefinished with data input, the trader may indicate that it is ready toproceed to the next phase, for example, by checking a “MIDS & POSITIONSSUBMITTED” box as shown in FIG. 11.

Once all traders have signaled that they are done with uploading theirrisk positions or as soon as the submission phase ends, the tradingsystem may automatically calculate auction price levels (DNA mids) anddelta values for each maturity date based on the traders' input. FIG. 11shows a screenshot of what the trader sees in a mid review phase, afterthe system has calculated DNA mids and delta values (or net notionals).Now, the second spreadsheet shows additional information compared to theprevious screen in FIG. 10. A DNA column now shows, next to thetrader-submitted mids, the DNA mids calculated by the system. To furtherassist the trader to decide whether to proceed with the trades, a numberof visual aids are provided on this screen. For example, thesystem-calculated DNA mids are plotted in the Curves chart in comparisonto the trader-submitted mids. The delta values are displayed for eachmaturity in a bar chart entitled “Delta Positions.”

Furthermore, the system may automatically calculate an implied profitand loss (P&L) value for each reference entity and/or each maturity datebased on the difference between the trader-submitted mids and the DNAmids. For example, the implied P&L may be the difference (between thetrader-submitted mids and the DNA mids) multiplied by the trader's deltavalue at that particular maturity. The implied P&L provides a convenientindication to the trader the potential profit or loss if the traderdecided to go forward with a trade at the DNA mid to reduce that deltaposition to zero. The further away the DNA mid is from thetrader-submitted mid, the larger the impact on the trader's P&L. Thus,the trader can quickly make a decision. If the trader decided not toproceed with a trade on a particular maturity, a corresponding checkboxin an “Exclude” column may be checked to opt out of that trade. Thisopt-out arrangement is more efficient and convenient for the tradersthan the traditional opt-in arrangements implemented in other electronictrading systems. As the trader checks or un-checks the Excludecheckboxes, the implied P&L totals in the first spreadsheet (on top sideof the screen) may update dynamically and the Curves and Delta Positionsgraphs may simultaneously indicate (e.g., in black triangles and blackbars respectively) which bucket has been excluded.

When the trader has finished reviewing the DNA mids and delta values,the trader may cheek a “DNA MIDS REVIEWED” checkbox. Once all tradershave finished the mid review or when the mid review period expires, aDNA auction algorithm may be run to match the risk positions. Then, inthe trade review phase, a list of the matched positions may bedisplayed, such as in a DNA Auction Trade Summary screen in FIG. 12.Here, each trader can review the trades generated through the DNAauction algorithm. To facilitate this review, one or more actual P&Lvalues may be calculated and displayed to the trader. The actual P&L maybe calculated on a per credit basis and/or a per delta neutral switchbasis. For example, the actual P&L may be the difference between thetrader-submitted mid and the DNA mid, multiplied by the delta valuereduced by the DNA algorithm. If the trader does not want to complete atrade, the trader may indicate as such in an Edit Trade column. Ifeither party to a particular trade backs out, then the trade will not bebooked. When any trade is cancelled or withdrawn in the trade reviewphase, the corresponding actual P&L may be updated in a main screen asshown in FIG. 13. The actual P&L values for the individual maturitydates are displayed in the second spreadsheet. The total actual P&Lvalues for the reference entities are displayed in the first spreadsheeton the top side of the screen. In addition, the Delta Positions graphmay indicate the change in delta value and the remaining delta value foreach maturity date, providing a visual illustration of potential impacton the trader's delta positions. Once a trader has finished reviewingthe trades, a “TRADES REVIEWED” checkbox may be checked in either theDNA Auction Trade Summary screen (FIG. 12) or the trade review mainscreen (FIG. 13).

Once all the traders have finished their trade review or upon expirationof the trade review period, the trades not cancelled or withdrawn may beexecuted and the resultant transaction data may be forwarded forstraight-through-processing (STP). Alternatively, a list of executedtrades can be exported from the DNA application or the online tradingsystem.

While the foregoing description includes many details and specificities,it is to be understood that these have been included for purposes ofexplanation only, and are not to be interpreted as limitations of thepresent invention. It will be apparent to those skilled in the art thatother modifications to the embodiments described above can be madewithout departing from the spirit and scope of the invention.Accordingly, such modifications are considered within the scope of theinvention as intended to be encompassed by the following claims andtheir legal equivalents.

1. A computer-implemented method for reducing delta values of creditrisk positions in an online trading system of credit derivatives, themethod comprising: receiving, in the online trading system of creditderivatives, a plurality of credit risk positions submitted by aplurality of trader clients, each credit risk position having a deltavalue and a maturity date, wherein each trader client's submission isunknown to other trader clients: identifying, from the plurality oftrader clients, at least two trader clients who hold offsetting creditrisk positions on at least two maturity dates; determining delta offsetsto be applied to delta values of the credit risk positions held by theat least two trader clients and having the at least two maturity dates,such that an overall delta of each of the at least two trader clients'credit risk positions remains substantially unchanged after theapplication of the delta offsets; calculating, based on the determineddelta offsets, notional amounts of credit derivative trades needed torealize the delta offsets; and executing the credit derivative tradesamong the at least two trader clients.
 2. The method according to claim1, further comprising: designating a single sector of credit derivativesfor a delta neutral auction session.
 3. The method according to claim 1,further comprising: inviting the plurality of trader clients to uploadthe plurality of credit risk positions to the online trading system ofcredit derivatives.
 4. The method according to claim 3, wherein theplurality of credit risk positions are uploaded to the online tradingsystem of credit derivatives in a spreadsheet format.
 5. The methodaccording to claim 3, further comprising: inviting the plurality oftrader clients to upload one or more prices associated with theplurality of credit risk positions, the one or more prices beingselected from a group consisting of: a bid price, an offer price, and asuggested mid price.
 6. The method according to claim 3, whereininformation associated with each of the plurality of credit riskpositions uploaded includes: a reference entity name; a seniority level;a maturity date; and an amount that reflects either a delta position atthe maturity date or an equivalent net CDS notional amount.
 7. Themethod according to claim 1, further comprising: receiving, from theplurality of trader clients, delta values of the plurality of creditrisk positions.
 8. The method according to claim 1, further comprising:calculating, by the online trading system, delta values of the pluralityof credit risk positions.
 9. The method according to claim 1, furthercomprising: identifying a first trader client and a second traderclient, wherein the first trader holds a first credit risk position thatat least partially offsets a second credit risk position held by thesecond trader client, the first and second credit risk positions sharinga first maturity date, wherein the first trader holds a third creditrisk position that at least partially offsets a fourth credit riskposition held by the second trader client, the third and fourth creditrisk positions sharing a second maturity date, and wherein the firstcredit risk position at least partially offsets the third credit riskposition and the second credit risk position at least partially offsetsthe fourth credit risk position.
 10. The method according to claim 9,further comprising: determining delta values for the first, second,third, and fourth credit risk positions; and causing each of the deltaoffsets to have the smallest absolute delta value out of the deltavalues.
 11. The method according to claim 1, further comprising:filtering out a subset of the plurality of credit risk positions thathave absolute delta values below a predetermined threshold.
 12. Themethod according to claim 1, further comprising: determining, by theonline trading system of credit derivatives, one or more price levelsfor executing the credit derivative trades among the at least two traderclients.
 13. The method according to claim 12, wherein the one or moreprice levels are determined based on a third-party benchmark.
 14. Themethod according to claim 12, wherein the one or more price levels aredetermined in a mid-fixing process based on bid and offer pricessubmitted by at least some of the plurality of trader clients.
 15. Themethod according to claim 12, wherein the one or more price levels aredetermined based on suggested mid prices submitted by at least some ofthe plurality of trader clients.
 16. The method according to claim 1,further comprising: offering a trader client an opportunity to opt outof a potential trade involving a credit risk position.
 17. The methodaccording to claim 1, further comprising: calculating a profit and loss(P&L) value for a trader client based on a difference between asuggested mid price submitted by the trader client and a price leveldetermined by the online trading system of credit derivatives.
 18. Themethod according to claim 1, further comprising: providing one or morevisual aids to the trader client via a graphical user interface (GUI),the visual aids being selected from a group consisting of: (1) one ormore informational spreadsheets displaying credit risk positions, pricelevels, and profit and loss (P&L) values: and (2) one or more graphsdisplaying price levels, delta values, or changes thereof.
 19. Themethod according to claim 1, further comprising: limiting a maximum gapbetween the at least two maturity dates.
 20. The method according toclaim 1, further comprising: querying each trader client to determinehow that trader client views positive and negative signs of a deltavalue in relation to buy or sell transactions; and processing creditrisk positions submitted by that trader client in a manner consistentwith the query result.
 21. An electronic trading system of creditderivatives, the system comprising: a processor; at least one storagedevice coupled to the processor; a user interface coupled to theprocessor via one or more communication networks; wherein the processoris adapted to communicate with the at least one storage device and theuser interface to execute instructions to perform the following tasks:receiving, in the online trading system of credit derivatives, aplurality of credit risk positions submitted by a plurality of traderclients, each credit risk position having a delta value and a maturitydate, wherein each trader client's submission is unknown to other traderclients; identifying, from the plurality of trader clients, at least twotrader clients who hold offsetting credit risk positions on at least twomaturity dates; determining delta offsets to be applied to delta valuesof the credit risk positions held by the at least two trader clients andhaving the at least two maturity dates, such that an overall delta ofeach of the at least two trader clients' credit risk positions remainssubstantially unchanged after the application of the delta offsets;calculating, based on the determined delta offsets, notional amounts ofcredit derivative trades needed to realize the delta offsets; andexecuting the credit derivative trades among the at least two traderclients.